Open Access
Add to BibSonomy
Abstract
This study introduces what we believe to be a novel photonic crystal fiber sensor utilizing surface plasmon resonance (SPR), incorporating four gold nanowires to enhance sensing capabilities. The research employs machine learning, specifically artificial neural networks (ANN), to predict confinement loss and sensitivity, achieving high accuracy without needing the imaginary part of the effective refractive index. The machine learning technique is applied in three different scenarios, resulting in mean squared errors of 0.084, 0.002, and 0.003, highlighting the reliability of the ANN models in predicting sensor outputs. Additionally, the sensor demonstrates impressive wavelength sensitivities of 2000-18000 nm/RIU (nanometers per refractive index unit) for refractive indices of 1.31-1.4 within the 720-1280 nm wavelength range, and a notable maximum amplitude sensitivity of 889.89 RIU-1. This integration of SPR, photonic crystal fiber, and machine learning not only optimizes sensor performance but also offers an efficient methodology for prediction, showcasing the potential of machine learning in advancing optical sensor design.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Surface plasmon resonance (SPR)-based photonic crystal fiber (PCF) sensors have drawn massive attention in recent years due to their remarkable advantages over traditional sensor platforms, including enhanced sensitivity, real-time detection, label-free sensing, high birefringence, reduced size and multi-parameter functionality [1–3]. Simultaneously, SPR plays an important role in overcoming the diffraction limit, a crucial advancement in optical technology. The diffraction limit restricts the localization of electromagnetic waves in dielectric media to regions larger than their wavelength, posing challenges for miniaturization. However, SPR leverages materials with negative dielectric permittivity, specifically metals below the plasma frequency. In these materials, metallic structures direct surface plasmon–polariton (SPP) modes, involving collective oscillations of electron plasma. This enables the localization of electromagnetic energy into nanoscale areas, effectively surpassing the diffraction limit [4–7]. The SPR phenomenon can be created by applying metal or metal oxide, either within the air holes of the PCF or on its external surface [8–10].
As metal films are prone to oxidation, falling off over time, and decreasing stability, the fabrication and performance of PCF-SPR sensors can be improved by depositing nanoscale layers of graphene on the surface of plasmonic material or applying plasmonic nanowires into PCF sensor configuration [11–13].
Zhan et al. proposed a refractive index sensor that utilizes a microfiber coated with gold nanowires, demonstrating superior performance compared to the sensor employing a gold film structure [14]. Yan et al. reported a sensor utilizing metal nanorods in a photonic crystal fiber, achieving a maximum spectral sensitivity of 9200 nm/RIU [15]. Liu et al. designed and investigated an ex-centric core photonic crystal fiber sensor with gold nanowires with a maximum spectral sensitivity of 14200 nm/RIU [16]. In 2020, a high-sensitivity D-type PCF sensor based on a metal nanowire array for analyte RI range from 1.32 to 1.38 was studied by Tong et al. This work reports a maximum sensitivity of 16000 nm/RIU [17]. Also, Li et al. suggested a D-shaped photonic crystal fiber sensor employing gold nanowires, demonstrating a maximum sensitivity of 19699 nm/RIU [18].
Artificial neural networks (ANNs) can be used to design and analyze optical components, particularly in the field of photonics. They offer high speed and efficiency in predicting the fundamental parameters of photonic crystal (PC) resonant cavities [19]. ANNs can be utilized to significantly expedite the prediction of numerical simulation outcomes. Zelaci et al. proposed the use of generative adversarial networks (GAN) to augment the real dataset and train an ANN model for predicting confinement loss in PCF [20]. An ANN/MLP model is used to calculate the effective mode area, dispersion, effective index, and confinement loss of a photonic crystal fiber. It is discussed that the presented model can predict the output for unknown devices faster than simulation and numerical analysis [21]. A highly sensitive PCF-based surface plasmon resonance sensor for detecting cancerous cells with a thin layer of Au/$\textrm{MXene}$ is reported by Kumar et al. in which the machine learning approach is applied to predict sensor sensitivity and effective refractive index for core mode with mean squared of 0.01525 [22]. Mezzi et al. developed an artificial neural network model to predict the output pulse shape parameters for a ring cavity fiber laser incorporating PCF [23]. Moreover, deep neural networks have been used for plasmonic sensor modeling and optimization. These networks can accurately capture the complex relationship between plasmonic geometry and its optical properties, such as resonance spectra, near-field enhancement, and far-field spectrum [24–26].
Herein, a novel PCF sensor is presented that harnesses the power of surface plasmon resonance (SPR) and incorporates four gold nanowires to achieve remarkable sensing capabilities. Our motive is to develop and train a neural network capable of quickly estimating both sensitivity and confinement loss for a given sensor structure. The sensor is analyzed through COMSOL Multiphysics software, focusing on analytes with refractive indices ranging from 1.31 to 1.4. The sensor demonstrates a maximum sensitivity of 889.89 1/RIU and wavelength sensitivities ranging from 2000 to 18000 nm/RIU for refractive indices between 1.31 and 1.4 within the 720-1280 nm wavelength range. Then, machine learning is used to study the performance of the proposed PCF sensor and predict confinement loss and sensitivity. In the first scenario, the input of the neural network is wavelength, analyte refractive index, imaginary part of the effective refractive index, and radius of the air nanowires, and the output of the neural network is the confinement loss and sensitivity. This dataset was collected using Comsol software. Considering that the imaginary part of the effective refractive index is a component that is obtained through the Comsol software, in the second and third scenarios, to reduce the need for the Comsol software and save time, the imaginary part of the effective refractive index from the input of neural network has been removed. It can be seen that without the need for this component, the neural network can predict the confinement loss and sensitivity and provide a comparison between these two components for different values of the radius of the gold nanowire. As a result, once trained, the proposed model provides a quick and efficient way to estimate the sensitivity and confinement loss for a given sensor configuration. This can save time and resources compared to traditional simulation methods.
2. Design and numerical analysis
As demonstrated in Fig. 1, the photonic crystal fiber sensor consists of two rings of air holes in the hexagonal arrangement. The innermost ring is a complete ring with six air holes. Four holes are omitted in the next ring to create four open channels to locate four gold nanowires with a diameter of ${d_g} = 1\; \mathrm{\mu} \textrm{m}$.
To facilitate sensor fabrication, gold nanowires are utilized in place of gold layers which will prevent the problematic metal deposition process. For the purpose of considering the fiber core and capturing the light in its center, an air hole is removed from the center. The other structural parameters are assumed to be $d = 0.6\; \mathrm{\mu} \textrm{m}$, ${d_1} = \; 1.6\; \mathrm{\mu} \textrm{m}$, and $\mathrm{\Lambda } = 2\,\mathrm{\mu}\textrm{m}$. A layer with a thickness of 1.5 $\mathrm{\mu}\textrm{m}$ contains the analyte. As a perfectly matched layer (PML) with a thickness of 1.5 $\mathrm{\mu}\textrm{m}$ has been established, the simulation and calculation results have improved.
The fused silica is considered as the background material. The refractive index of this material can be defined by the Sellmeier equation [27]:
To calculate the performance parameters of the sensor, the confinement loss is a key factor to consider that is defined by the following equation [29]:
The sensing performance of the proposed PCF-based SPR sensor can be evaluated by wavelength interrogation and amplitude interrogation methods. By using these methods, wavelength sensitivity (spectral sensitivity) and amplitude sensitivity can be calculated, respectively [30]. Wavelength sensitivity can be obtained by [31]:
3. Simulation results and performance analysis
For investigation of the sensing performance of the proposed photonic crystal fiber sensor, the operating principle of the PCF sensor should be analyzed. Figure 2(a)-(c) shows the magnetic field distribution of the x-polarized fundamental core, SPP, and coupled modes, respectively.
Fig. 2. The magnetic field distribution of x-polarized (a) fundamental core, (b) SPP mode, and (c) coupled mode.
In comparison with y-polarization, the x-polarization offers better coupling features. Therefore, x-polarization is chosen for further consideration. The confinement loss spectrum and the dispersion relation between core and SPP modes are shown in Fig. 3 for ${n_a} = 1.38$. As can be observed from this figure, the phase matching condition takes place at the resonance wavelength of $1\; \mathrm{\mu}\textrm{m}$, where the real part of effective refractive indices of core and SPP modes are equal. At this point, a loss peak of 358.82 dB/cm can be seen.
Figure 4 illustrates the spectra of confinement loss across a broad spectrum of analyte refractive indices, ranging from 1.31 to 1.4 with the step of 0.01. By increasing the analyte refractive index, the loss curves shift toward higher wavelengths which is called red shift. According to this figure, the highest loss is 521.56 dB/cm for ${n_a} = 1.4$ and the lowest loss is 60 dB/cm for ${n_a} = 1.31$.
According to Fig. 4, the corresponding resonance wavelength shifts are 20 nm for 1.31 to 1.32, 20 nm for 1.32 to 1.33, 40 nm for 1.33 to 1.34, 20 nm for 1.34 to 1.35, 60 nm for 1.35 to 1.36, 40 nm for 1.36 to 1.37, 80 nm for 1.37 to 1.38, 10 nm for 1.38 to 1.39, 180 nm for 1.39 to 1.4. Therefore, the wavelength sensitivities are obtained as 2000nm/RIU, 2000nm/RIU, 4000 nm/RIU, 2000nm/RIU, 6000 nm/RIU, 4000 nm/RIU, 8000 nm/RIU, 10000 nm/RIU, and 18000 nm/RIU.
The sensitivity of the proposed sensor with respect to the wavelength is illustrated in Fig. 5 with the variation of analyte RI from 1.31 to 1.39. The calculated amplitude sensitivities are 181.53 $\textrm{RI}{\textrm{U}^{ - 1}}$, 221.7 $\textrm{RI}{\textrm{U}^{ - 1}}$, 259.1 $\textrm{RI}{\textrm{U}^{ - 1}}$, 322.1 $\textrm{RI}{\textrm{U}^{ - 1}}$, 402.73 $\textrm{RI}{\textrm{U}^{ - 1}}$, 460.4 $\textrm{RI}{\textrm{U}^{ - 1}}$, 746.44 $\textrm{RI}{\textrm{U}^{ - 1}}$, 889.89 $\textrm{RI}{\textrm{U}^{ - 1}}$, and 873.61 $\textrm{RI}{\textrm{U}^{ - 1}}$. Therefore, the maximum sensitivity is 889.89 $\textrm{RI}{\textrm{U}^{ - 1}}$ for an analyte RI variation of 1.38-1.39.
As a key parameter, the resolution values of the suggested sensor structure are studied, too. The calculated maximum resolution is $5.56\; \times {10^{ - 6}}$ RIU, which indicates the ability of the sensor to detect subtle changes in refractive index. Moreover, based on Eq. (7), the FOM values as 45.55 $\textrm{RI}{\textrm{U}^{ - 1}}$, 4.48 $\textrm{RI}{\textrm{U}^{ - 1}}$, 7.85 $\textrm{RI}{\textrm{U}^{ - 1}}$, 42.37 $\textrm{RI}{\textrm{U}^{ - 1}}$, 10.69 $\textrm{RI}{\textrm{U}^{ - 1}}$, 7.19 $\textrm{RI}{\textrm{U}^{ - 1}}$, 147.6 $\textrm{RI}{\textrm{U}^{ - 1}}$, 210.08 $\textrm{RI}{\textrm{U}^{ - 1}}$, and 311.41 $\textrm{RI}{\textrm{U}^{ - 1}}$ are achieved for 1.31, 1.32, 1.33, 1.34, 1.35, 1.36, 1.37, 1.38, and 1.39, respectively. Figure 6 shows the polynomial regression results of the proposed sensor. This figure illustrates the resonance wavelength with respect to the analyte refractive index. The fitting curve equation with ${\textrm{R}^2} = 0.9838$ is obtained as below:
In this section, the architecture parameters of the artificial neural network and the generated dataset for the study are discussed. An ANN with 3 hidden layers and 50 neurons in each layer is modeled. In the first scenario, the input variables of the collected dataset are wavelength (λ = 0.6 to 1.4), analyte refractive index (${n_a} = $ 1.31 to 1.39), imaginary part of the effective refractive index, and radius of the gold nanowires (${r_g} = $ 0.3 µm to 0.6 µm) together with their second, third, and fourth powers. Adding higher powers of input parameters to a dataset is known as feature engineering. This technique enhances machine learning models by capturing non-linear relationships, increasing flexibility, and improving predictive performance [35]. The output variables are confinement loss and sensitivity. The finite labeled dataset is obtained through the numerical study conducted using finite element method (FEM) in Comsol Multiphysics software.
Adaptive moment estimation (Adam) optimizer and rectified linear unit (ReLU) activation function were employed to optimize the weights and biases and introduce non-linear properties to the ANN [36]. The training process of the ANN model consists of many epochs to update the synaptic weights and biases in order to reduce the error between predicted and desired target outputs. As an important concept, the epoch refers to a single pass through the entire training dataset during the training process. The models were trained for 1000 epochs. After each epoch, the discrepancy between the predicted output and the target outputs is computed using the mean squared error (MSE) loss function [29,37,38].
1476 data were provided after preprocessing of data. In the first scenario, a set of 369 data about sensor with ${r_g} = $ 0.3 µm was specifically allocated for testing and the training dataset comprises 885 data associated with sensors with ${r_g} = $ 0.4 µm, 0.5 µm, and 0.6 µm. Consequently, the model has not been exposed to any data related to ${r_g} = $ 0.3 µm. Here, we aim to assess the model to predict the value of confinement loss and sensitivity for a sensor with a new value of ${r_g}\; $(${r_g} = $ 0.3 µm). The graphical representation of the mean squared error (MSE) for both the training and validation datasets is illustrated in Fig. 7. The MSE loss function is calculated after each epoch between the predicted value and the actual value and according to the backpropagation phenomenon, the weights of the hidden layers are updated regularly. The MSE values for the training dataset and validation dataset decreased during 1000 epochs and they reached below 0.0005 and 0.0006, respectively.
After training the model with the training dataset and evaluating it with the validation dataset, the performance of the neural network is checked using a test dataset to assess how well the model is expected to perform on unseen data. The MSE value for the test dataset is 0.084, which underscores the capability of the model to make accurate predictions for new input values. The sensitivity and confinement loss diagrams for actual and predicted datasets are demonstrated in Figs. 8(a) and 8(b) which represent the performance of the model.
Figures 9(a) and 9(b) represent the scatter plots illustrating the relationship between predicted and actual data, accompanied by training, validation, test datasets, and regression lines. The predicted values are generated by an ANN model, while the actual values are provided by simulation software.
Fig. 9. The scatter plot of predicted and actual (a) sensitivity and (b) confinement loss values in logarithm.
In the second scenario, 369 data related to the sensor with ${r_g} = $ 0.4 µm were dedicated to the test and the training data includes 1107 data related to the sensor with ${r_g} = $ 0.3 µm, 0.5 µm, and 0.6 µm. Therefore, the model has never encountered data related to ${r_g} = $ 0.4 µm. It is noteworthy that unlike the previous scenario, in the following scenarios imaginary part of the effective refractive index is deleted from input variables in order to determine whether the ANN model can predict confinement loss and sensitivity without requiring data from simulation software. The mean squared error (MSE) plot for training and validation datasets is shown in Fig. 10. The MSE values for training and validation datasets decreased during 1000 epochs and they reached below 0.005 and 0.003 respectively.
Here, the test dataset only includes data related to the sensor with ${r_g} = $ 0.4 µm, and the model has not been trained with ${r_g} = $ 0.4 µm. At this stage, we aim to see whether the model is able to graphically estimate loss and sensitivity for a new value of gold wire radius (${r_g} = $ 0.4 µm) that it has never seen before. The MSE value for test dataset is 0.002 which shows that the trained model can generalize well to unseen data and is able to predict outputs for new input values.
Figures 11(a) and 11(b) present the sensitivity and loss diagram for actual and predicted datasets (${r_g} = $ 0.4 µm for nine different values of analyte refractive index which was not present in the training dataset) which makes it possible to compare the actual and predicted data. According to these diagrams, the proposed neural network is able to predict well the new data that it has not seen before. Figure 12 shows the graphs of predicted and actual data with regression line for the training, validation and test datasets for the two output parameters loss and wavelength sensitivity.
Fig. 11. (a) Confinement loss and (b) sensitivity for different analyte refractive index (${n_a} = 1.31\; to\; {n_a} = 1.39$).
Figures 13(a) and 13(b) show the actual and predicted data of confinement loss and sensitivity for ${r_g}$= 0.3, 0.4, 0.5, 0.6 $\mathrm{\mu}\textrm{m}$ from left to right when na = 1.31, respectively. So, comparing the sensitivity and loss of the suggested sensor is feasible for the refractive index ${n_a}$ = 1.31 across four different values of gold nanowires radius (0.3, 0.4, 0.5, 06 $\mathrm{\mu}\textrm{m}$). As a result, a better radius that improves these two components can be selected. This comparison is available for all values of the refractive index of the analyte, and this investigation can be performed for any value of the refractive index of the analyte.
Fig. 13. (a) Confinement loss and (b) sensitivity for ${n_a} = 1.31$ and ${r_g} = 0.3\; \mathrm{\mu} m,\; {r_g} = 0.4\; \mathrm{\mu} m,\; {r_g} = 0.5\; \mathrm{\mu} m,\; and\; {r_g} = 0.6\; \mathrm{\mu} m$, respectively.
In the third scenario, 1312 data related to the sensor with ${r_g} = $ 0.3, 0.4, 0.5, 0.6 µm were dedicated to the training dataset, and 164 data were randomly chosen among data related to the sensor with ${r_g} = $ 0.3, 0.4, 0.5, 0.6 µm for the test dataset. Here, we aim to determine if the ANN can visually estimate confinement loss and sensitivity for random values of ${r_g}$ among 0.3, 0.4, 0.5, 0.6 µm and ${n_a}$ among 1.31, 1.32, 1.33, 1.34, 1.35, 1.36, 1.37, 1.38, 1.39 without requiring data from simulation software. The mean squared error (MSE) plot for the training dataset and validation dataset are shown in Fig. 14. The MSE values for the training dataset and validation dataset decreased during 1000 epochs and they reached below 0.003 and 0.006 respectively.
Here, the test dataset includes 164 data randomly chosen from collected data and they were unseen to the model during the training process. The random test dataset include data related to (${n_a} = 1.31\; ,\; {r_g} = 0.4\; \mathrm{\mu}\textrm{m}$), (${n_a} = 1.35\; ,\; {r_g} = 0.5\; \mathrm{\mu}\textrm{m}$), (${n_a} = 1.38\; ,\; {r_g} = 0.4\; \mathrm{\mu}\textrm{m}$), and (${n_a} = 1.38\; ,\; {r_g} = 0.\; 6\; \mathrm{\mu}\textrm{m}$) features. The sensitivity and confinement loss diagram for actual and predicted datasets which offers the possibility to compare actual data and the data predicted by ANN are illustrated in Figs. 15(a) and 15(b). The MSE value for test dataset is 0.003. Accordingly, the proposed model makes a good prediction on the test dataset.
Fig. 15. (a) Confinement loss and (b) sensitivity for four random data: (${n_a}$=1.31, ${r_g}$=0.4 µm), (${n_a}$=1.35, ${r_g}$=0.5 µm), (${n_a}$=1.38, ${r_g}$=0.4 µm), and (${n_a}$=1.38, ${r_g}$=0.6 µm), respectively.
Figures 16(a) and 16(b) show the scatter plot of predicted and actual data with regression lines for the training, validation, and test datasets for the two output parameters loss and sensitivity.
4. Conclusion
In summary, this study introduces an innovative surface plasmon resonance-based photonic crystal fiber sensor with four gold nanowires. Leveraging the predictive power of artificial neural networks, we achieved precise estimations of confinement loss and sensitivity, showcasing mean squared errors of 0.084, 0.002, and 0.003 in distinct scenarios, underscores the potential of machine learning in advancing the field of optical sensor design. Our numerical analysis using COMSOL Multiphysics software confirms the sensor's exceptional performance, with an impressive amplitude sensitivity of 889.89 1/RIU and wavelength sensitivities ranging from 2000 to 18000 nm/RIU within the 720-1280 nm wavelength range for refractive indices between 1.31 and 1.4. The seamless integration of surface plasmon resonance, photonic crystal fiber, and machine learning not only optimizes sensor performance but also establishes an efficient and resource-saving methodology for predictive modeling. The streamlined modeling process, particularly in scenarios excluding the imaginary part of the effective refractive index, offers a quick and resource-efficient means of estimating sensor characteristics for various configurations. This contributes to the advancement of optical sensing technologies, enhancing their efficiency and precision.
Funding
Shahid Rajaee Teacher Training University (4976).
Acknowledgments
This research has been done in Nano-photonics and Optoelectronics Research Laboratory (NORLab).
Disclosures
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Author's Contributions. A. E. and A. R: designed and performed simulations and analyzed data, A. B.: reviewed and edited, S. O.: supervised, verified, edited, and prepared the final draft of the manuscript. All authors read and approved the final manuscript.
Data availability
The code and dataset for our research are available on a public repository on GitHub at [39].
References
1. S. Mittal, T. Sharma, M. Tiwari, et al., “Surface plasmon resonance based photonic crystal fiber biosensors: A review,” Mater. Today: Proc. 43, 3071–3074 (2021). [CrossRef]
2. C. Liu, J. Wang, F. Wang, et al., “Surface plasmon resonance (SPR) infrared sensor based on D-shape photonic crystal fibers with ITO coatings,” Opt. Commun. 464, 125496 (2020). [CrossRef]
3. Y. Lu, C.-J. Hao, B.-Q. Wu, et al., “Grapefruit fiber filled with silver nanowires surface plasmon resonance sensor in aqueous environments,” Sensors 12(9), 12016–12025 (2012). [CrossRef]
4. D. Gramotnev and S. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010). [CrossRef]
5. A. Farmani, A. Mir, and Z. Sharifpour, “Broadly tunable and bidirectional terahertz graphene plasmonic switch based on enhanced Goos-Hänchen effect,” Appl. Surf. Sci. 453, 358–364 (2018). [CrossRef]
6. R. Krishnamoorthy, I. Soubache, and A. Farmani, “Exploring surface plasmon resonance ring resonator structure for high sensitivity and ultra-high-Q optical filter with FDTD method,” Opt. Quantum Electron. 54(2), 75 (2022). [CrossRef]
7. Z. Salehnezhad, M. Soroosh, and A. Farmani, “Design and numerical simulation of a sensitive plasmonic-based nanosensor utilizing MoS2 monolayer and graphene,” Diamond Relat. Mater. 131, 109594 (2023). [CrossRef]
8. M. Chauhan and V. K. Singh, “Fiber optic plasmonic sensors based on theoretical analysis: A review,” Opt. Quantum Electron. 53(7), 409 (2021). [CrossRef]
9. A. Farmani, M. Farhang, and M. H. Sheikhi, “High performance polarization-independent Quantum Dot Semiconductor Optical Amplifier with 22 dB fiber to fiber gain using Mode Propagation Tuning without additional polarization controller,” Opt. Laser Technol. 93, 127–132 (2017). [CrossRef]
10. S. Khani, A. Farmani, and A. Mir, “Reconfigurable and scalable 2,4-and 6-channel plasmonics demultiplexer utilizing symmetrical rectangular resonators containing silver nano-rod defects with FDTD method,” Sci. Rep. 11(1), 13628 (2021). [CrossRef]
11. Q. Liu, Z. Ma, Q. Wu, et al., “The biochemical sensor based on liquid-core photonic crystal fiber filled with gold, silver and aluminum,” Opt. Laser Technol. 130, 106363 (2020). [CrossRef]
12. A. A. Rifat, M. R. Hasan, R. Ahmed, et al., “Photonic crystal fiber-based plasmonic biosensor with external sensing approach (erratum),” J. Nanophotonics 12(01), 1 (2018). [CrossRef]
13. D. Wang, Y. Zhang, Y. Qi, et al., “Tunable surface plasmon resonance sensor based on graphene-coated photonic crystal fiber in terahertz,” Appl. Opt. 61(22), 6664–6670 (2022). [CrossRef]
14. Y. Zhan, Y. Li, Z. Wu, et al., “Surface plasmon resonance-based microfiber sensor with enhanced sensitivity by gold nanowires,” Opt. Mater. Express 8(12), 3927–3940 (2018). [CrossRef]
15. X. Yan, B. Li, T. Cheng, et al., “Analysis of High Sensitivity Photonic Crystal Fiber Sensor Based on Surface Plasmon Resonance of Refractive Indexes of Liquids,” Sensors 18(9), 2922 (2018). [CrossRef]
16. C. Liu, G. Fu, F. Wang, et al., “Ex-centric core photonic crystal fiber sensor with gold nanowires based on surface plasmon resonance,” Optik 196, 163173 (2019). [CrossRef]
17. K. Tong, Z. Cai, J. Wang, et al., “D-type photonic crystal fiber sensor based on metal nanowire array,” Optik 218, 165010 (2020). [CrossRef]
18. W. Li, Y. Chen, J. Xu, et al., “A D-Shaped SPR-Based PCF Sensor with an Extremely High-Amplitude Sensitivity for Measuring the Refractive Index,” Micromachines 14(7), 1295 (2023). [CrossRef]
19. S. Jia, Z. Zhou, and L. Cao, “Design of Terahertz One-dimensional Photonic Crystal Cavity Based on Neural Network and Optimization Algorithm,” in 2022 47th International Conference on Infrared, Millimeter and Terahertz Waves (IRMMW-THz), 2022, pp. 1–2.
20. A. Zelaci, A. Yasli, C. Kalyoncu, et al., “Generative Adversarial Neural Networks Model of Photonic Crystal Fiber Based Surface Plasmon Resonance Sensor,” J. Lightwave Technol. 39(5), 1515–1522 (2021). [CrossRef]
21. S. Chugh, A. Gulistan, S. Ghosh, et al., “Machine learning approach for computing optical properties of a photonic crystal fiber,” Opt. Express 27(25), 36414–36425 (2019). [CrossRef]
22. A. Kumar, P. Verma, and P. Jindal, “Surface plasmon resonance sensor based on MXene coated PCF for detecting the cancer cells with machine learning approach,” Microelectron. Eng. 267-268, 111897 (2023). [CrossRef]
23. R. Mezzi, F. Bahloul, A. S. Karar, et al., “Predicting behavior of photonic crystal fiber lasers using artificial neural networks,” Opt. Commun. 542, 129582 (2023). [CrossRef]
24. X. Li, J. Shu, W. Gu, et al., “Deep neural network for plasmonic sensor modeling,” Opt. Mater. Express 9(9), 3857–3862 (2019). [CrossRef]
25. Q. Wu, X. Li, L. Jiang, et al., “Deep neural network for designing near- and far-field properties in plasmonic antennas,” Opt. Mater. Express 11(7), 1907–1917 (2021). [CrossRef]
26. D. Mortazavi, A. Kouzani, and L. Matekovits, “Modeling LSPR nano-particles by using neural networks,” BODYNETS 2014 - 9th Int. Conf. Body Area Networks, pp. 316–319, Nov. 2014.
27. J. Wang, C. Liu, F. Wang, et al., “Surface plasmon resonance sensor based on coupling effects of dual photonic crystal fibers for low refractive indexes detection,” Results Phys. 18, 103240 (2020). [CrossRef]
28. A. Shafkat, “Analysis of a gold coated plasmonic sensor based on a duplex core photonic crystal fiber,” Sens. Bio-Sensing Res. 28, 100324 (2020). [CrossRef]
29. N. Sakib, S. Arafin, Z. Anis, et al., “Design and analysis of a highly sensitive modified square structure dual slotted single core plasmonic biosensor,” Opt. Continuum 1(2), 143–160 (2022). [CrossRef]
30. R. Hasan, S. Akter, A. Rifat, et al., “A Highly Sensitive Gold-Coated Photonic Crystal Fiber Biosensor Based on Surface Plasmon Resonance,” Photonics 4(4), 18 (2017). [CrossRef]
31. H. Pakarzadeh, V. Sharif, D. Vigneswaran, et al., “Graphene-assisted tunable D-shaped photonic crystal fiber sensor in the visible and IR regions,” J. Opt. Soc. Am. B 39(6), 1490–1496 (2022). [CrossRef]
32. M. B. A. S. S. Hossain, Md Shafayet Hossain, S.M. Riazul Islam, et al., “Numerical development of high performance quasi D-shape PCF-SPR biosensor: An external sensing approach employing gold,” Results Phys. 18, 103281 (2020). [CrossRef]
33. A. Shafkat, M. I. Reja, M. J. Miah, et al., “Numerical exploration of external sensing scheme based photonic crystal fiber surface plasmonic sensor with different noble plasmonic materials and their alloys,” Optik 231, 166418 (2021). [CrossRef]
34. M. T. Rahman, S. Datto, and M. N. Sakib, “Highly sensitive circular slotted gold-coated micro channel photonic crystal fiber based plasmonic biosensor,” Opt. Continuum 4(6), 1808–1826 (2021). [CrossRef]
35. C. O’Sullivan, “The power of feature engineering,” towards data science. Medium, 2021. https://towardsdatascience.com/the-power-of-feature-engineering-b6f3bb7de39c.
36. A. D. Rasamoelina, F. Adjailia, and P. Sinčák, “A Review of Activation Function for Artificial Neural Network,” in 2020 IEEE 18th World Symposium on Applied Machine Intelligence and Informatics (SAMI), 2020, pp. 281–286.
37. D. Svozil, V. Kvasnicka, and J. Pospichal, “Introduction to multi-layer feed-forward neural networks,” Chemom. Intell. Lab. Syst. 39(1), 43–62 (1997). [CrossRef]
38. S. Lee, I. Park, and J.-K. Choi, “Spatial Prediction of Ground Subsidence Susceptibility Using an Artificial Neural Network,” Environ. Manage. 49(2), 347–358 (2012). [CrossRef]
39. Arefe Ehyaee, “ML-based-PCF-SPR-sensor,” GitHub (2023), https://github.com/Arefe-Ehyaee/ML-based-PCF-SPR-sensor.git.
